(abridged) We have analyzed the properties of the rest-frame optical emission lines of a sample of 53 intensely star forming galaxies at z=1.3 to 2.7 observed with SINFONI on the ESO-VLT. We find large velocity dispersions in the lines, sigma=30-250 km/s. Our data agree well with simulations where we applied beam-smearing and assumed a scaling relation of the form: velocity dispersion is proportional to the square root of the star-formation intensity (star-formation rate per unit area). We conclude that the dispersions are primarily driven by star formation. To explain the high surface brightness and optical line ratios, high thermal pressures in the warm ionized medium, WIM, are required (log P/k (K/cm^3)>~6-7). Such thermal pressures in the WIM are similar to those observed in nearby starburst galaxies, but occur over much larger physical scales. Moreover, the relatively low ionization parameters necessary to fit the high surface brightnesses and optical line ratios suggest that the gas is not only directly associated with regions of star formation, but is wide spread throughout the general ISM. Thus the optical emission line gas is a tracer of the large scale dynamics of the bulk of the ISM. We present a simple model for the energy input from young stars in an accreting galaxy, to argue that the intense star-formation is supporting high turbulent pressure, which roughly balances the gravitational pressure and thus enables distant gas accreting disks to maintain a Toomre disk instability parameter Q~1. For a star formation efficiency of 3%, only 5-15% of the mechanical energy from young stars that is deposited in the ISM is needed to support the level of turbulence required for maintaining this balance. Since this balance is maintained by energy injected into the ISM by the young stars themselves, this suggests that star formation in high redshift galaxies is self-regulating.
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